2007/07/05 by Uwe C. Tauber, Uwe Claus Täuber
Materials Science · Physics and Astronomy · #Material Dynamics and Properties #Theoretical and Computational Physics #cond-mat.stat-mech #stochastic dynamics and bifurcation
paper · pdf · doi:10.1007/978-0-387-30440-3_200
published as Encyclopedia of Complexity and Systems Science, Robert A. Meyers (ed.), Springer; New York, 2009; pp. 3360-3374 · Article for the Encyclopedia of Complexity and System Science, B. Meyers (Ed.), Springer-Verlag Berlin, 2008
arxiv created 2007/07/05 · openalex publication_date 2009/01/01 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/04
Many complex systems are characterized by intriguing spatio-temporal structures. Their mathematical description relies on the analysis of appropriate correlation functions. Functional integral techniques provide a unifying formalism that facilitates the computation of such correlation functions and moments, and furthermore allows a systematic development of perturbation expansions and other useful approximative schemes. It is explained how nonlinear stochastic processes may be mapped onto exponential probability distributions, whose weights are determined by continuum field theory actions. Such mappings are madeexplicit for (1) stochastic interacting particle systems whose kinetics is defined through a microscopic master equation; and (2) nonlinear Langevin stochastic differential equations which provide a mesoscopic description wherein a separation of time scales between the relevant degrees of freedom and background statistical noise is assumed. Several well-studied examples are introduced to illustrate the general methodology.